Lectures On Siegel Modular Forms And Representation By Quadratic Forms
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Lectures On Siegel Modular Forms And Representation By Quadratic Forms
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Author : Yoshiyuki Kitaoka
language : en
Publisher:
Release Date : 1986
Lectures On Siegel Modular Forms And Representation By Quadratic Forms written by Yoshiyuki Kitaoka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Siegel Modular Forms
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Author : Ameya Pitale
language : en
Publisher: Springer
Release Date : 2019-05-07
Siegel Modular Forms written by Ameya Pitale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the areaas a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Arithmetic Of Quadratic Forms
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Author : Yoshiyuki Kitaoka
language : en
Publisher: Cambridge University Press
Release Date : 1999-04-29
Arithmetic Of Quadratic Forms written by Yoshiyuki Kitaoka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-29 with Mathematics categories.
Provides an introduction to quadratic forms.
K Theory And Algebraic Geometry Connections With Quadratic Forms And Division Algebras
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Author : Bill Jacob
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
K Theory And Algebraic Geometry Connections With Quadratic Forms And Division Algebras written by Bill Jacob and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Volume 2 of two - also available in a set of both volumes.
Number Theory
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Author : H. Kisilevsky
language : en
Publisher: American Mathematical Soc.
Release Date :
Number Theory written by H. Kisilevsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered include algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation. The volume contains both research andexpository papers suitable for graduate students and researchers interested in number theory.
Modular Forms And Hecke Operators
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Author : A. N. Andrianov V. G. Zhuravlev
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-08-28
Modular Forms And Hecke Operators written by A. N. Andrianov V. G. Zhuravlev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-28 with Mathematics categories.
The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Modular Forms And Hecke Operators
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Author : A. N. Andrianov
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-29
Modular Forms And Hecke Operators written by A. N. Andrianov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-29 with categories.
he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Tata Lectures On Theta I
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Tata Lectures On Theta I written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions. These notes grew out of a series of lectures given at the Tata Institute of Fundamental Research in the period October, 1978, to March, 1979, on which notes were taken and excellently written up by C. Musili and M. Nori. I subsequently lectured at greater length on the contents of Chapter III at Harvard in the fall of 1979 and at a Summer School in Montreal in August, 1980, and again notes were very capably put together by E. Previato and M. Stillman, respectively. Both the Tata Institute and the University of Montreal publish lecture note series in which I had promised to place write-ups of my lectures there. However, as the project grew, it became clear that it was better to tie all these results together, rearranging and consolidating the material, and to make them available from one place. I am very grateful to the Tata Institute and the University of Montreal for permission to do this, and to Birkhauser-Boston for publishing the final result. The first 2 chapters study theta functions strictly from the viewpoint of classical analysis. In particular, in Chapter I, my goal was to explain in the simplest cases why the theta functions attracted attention.
Quadratic And Hermitian Forms
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Author : McMaster University
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Quadratic And Hermitian Forms written by McMaster University and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).
The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2009-09-02
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.